The Potential of the 7R-R Closed Loop Mechanism to Transfer Motion Between Two Shafts with Varying Angular Position

Transmission of the motion between two shafts can be obtained by a Double Cardan Joint (DCJ), which, under particular geometrical conditions, can be homokinetic. A DCJ can be regarded as a 7R closed loop mechanism, which highly reduce the technical/manufacturing complexity when compliant joints are used to replace the R revolute joints. The case of intersecting shaft axes with varying relative orientation is of particular interest in many applications and can be efficiently modeled by a symmetric 7R-R closed loop mechanism to get a homokinetic transmission. This paper deals with the analysis of a type of symmetric 7R-R mechanism, for the homokinetic motion transmission between two incident shafts. Specialized closure equations are wrote to obtain a closed-form solution of the position analysis. The analysis of both the radial envelope (which affects the mechanism size) and the mechanism singularities are conducted. In particular, a direct relation between the maximum value of the radial envelope and the angle between the shafts is presented. Moreover, the geometrical parameters that determine a singularity condition of the mechanism are found. The singularity configurations are also geometrically analyzed, which disclose the feature of the mechanism to evolve into two different configurations, namely a spherical 4R and a symmetric 7R mechanism. These results can be used for the mechanism dimensioning.